Method and computer program for performing scaffold design optimization for enhanced bone healing and method for manufacturing scaffolds

Abstract

The present invention relates to a method, particularly a computer-implemented method, for performing optimization of a scaffold design (h) for enhancing bone healing, comprising the steps of: a) inputting a set of parameters including information on the geometry and material of the scaffold (3) into a computational model, the computational model including a finite element model and a mechanobiology computational model, the finite element model determining a set of mechanical information data for the set of parameters and providing it to the mechanobiology computational model, the mechanobiology computational model determining a regenerated bone volume from the set of mechanical information data; b) determining a plurality of regenerated bone volumes for the set of parameters according to step a) to generate scaffold bone data relating the regenerated bone volumes to the corresponding set of parameters; c) determining a computational surrogate model consisting of an analytical equation configured to relate the regenerated bone volume to the set of parameters from the scaffold bone data; and d) determining from the computational surrogate model an optimal set of parameters for which the computational surrogate model outputs a maximum regenerated bone volume. The present invention also relates to a computer program and a method for manufacturing a scaffold (3).

Description

[Technical field]

[0001] The present invention relates to a method and computer program for performing an optimization of a scaffold design towards enhanced bone healing, and a method for manufacturing a scaffold designed using the method steps for performing the scaffold design. [Background technology]

[0002] Biomaterial scaffolds can be used as guide structures to promote bone regeneration in areas where large sections of bone are missing. For successful bone regeneration, cells need to be provided with an appropriate mechanical environment within the scaffold pores to produce the required extracellular matrix. As disclosed by Cipitria et al. (2012) and Pobloth et al. (2018), cell behavior within the scaffold pores is influenced by both mechanical and biological conditions and changes during the bone regeneration process.

[0003] Scaffold design has mainly relied on trial-and-error approaches in the past, but in recent years, as disclosed by Guest and Prevost (2006), Almeida and da Silva Bartolo (2010), Chen et al. (2011), Xiao et al. (2012), Dias et al. (2014), Wang et al. (2016), Langelaar (2016), Uth et al. (2017), and Metz et al. (2020), several research groups have adopted a more systematic approach using numerical or computational optimization methods to maximize or minimize certain properties, such as maximum stiffness; maximum permeability for good nutrient flow, etc. However, maximizing the mechanical properties of the scaffold does not necessarily guarantee better bone regeneration, since constructs that are too stiff have been shown to reduce bone regeneration, as disclosed by Pobloth et al. (2018) and Reznikov et al. (2019). Nevertheless, as disclosed by Petersen et al. (2018), construction of a scaffold mimicking defect tissue cannot be guaranteed to best support endogenous bone regeneration and osseointegration of the implant.

[0004] Scaffolds can be designed to achieve the same mechanical properties as the host tissue, as disclosed by Chang et al. (2017), Grbic and Comaniciu (2018), Hollister et al. (2003, 2002), and Sturm et al. (2010), or to withstand specific fatigue requirements, as disclosed by Pasini et al. (2014). However, this does not guarantee that the appropriate mechanical environment will be achieved within the scaffold pores. Another design strategy is to ensure appropriate mechanical properties within the scaffold pores immediately after implantation, as disclosed by Boccaccio et al. (2019, 2018) and Percoco et al. (2020).

[0005] Bone regeneration is a very dynamic process, and during the regeneration period, different types of tissues are formed, remodeled, and resorbed at specific locations, creating a mechanical environment that changes over time. This change in the mechanical environment in turn further influences tissue formation. Studies on spine fusion devices suggest that designs optimized for the immediate postoperative situation do not optimize subsequent bone formation, as disclosed by Bashkuev et al. (2015). As disclosed by Wu et al. (2021), an in silico comparison was performed between the bone regeneration outcomes of scaffolds optimized for the immediate postoperative situation and those that considered the same healing process to reach the same conclusion in 2D space, and as disclosed by Viateau et al. (2007) and Pobloth et al. (2018), identifying key design features of 3D scaffolds that support the regeneration of bone defects is difficult because biomaterial scaffolds are usually not used alone but are used in combination with bone grafting or BMP-2 to increase the success rate. It is believed that cells (preosteoblasts and / or osteogenic cells) that may be derived from bone grafts contribute to healing. Furthermore, as disclosed in Finkemeier (2002), bone grafts have osteoconductive properties (inducing new bone ingrowth) and osteoinductive properties (increasing bone deposition). However, how these different biostimulatory properties contribute, alone or in combination, to support the overall healing process has not yet been fully elucidated.

[0006] The numerical methods disclosed above are computationally expensive and often result in lengthy and cumbersome optimization processes that can take days or even weeks, which is prohibitive in a commercial environment. [Prior art documents] [Non-patent literature]

[0007] [Non-Patent Document 1] Almeida H de A, da Silva Bartolo PJ (2010) Virtual topological optimization of scaffolds for rapid prototyping. Medical Engineering & Physics 32:775–782. https: / / doi.org / 10.1016 / j.medengphy.2010.05.001

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[0008] The problem that the present invention seeks to solve is to provide a method for manufacturing a scaffold in a manner that enhances bone healing, along with a method and computer program that allows for accurate, yet rapid, optimization of scaffold design with the goal of enhancing bone healing. [Means for solving the problem]

[0009] This problem is solved by a method for performing a scaffold design optimization towards enhanced bone healing according to claim 1, a computer program according to claim 13 and a method for manufacturing a scaffold according to claim 14. Advantageous embodiments of the method for performing a scaffold design optimization towards enhanced bone healing are given in the dependent claims 2-12.

[0010] A first aspect of the present invention relates to a method, in particular a computer-implemented method, for performing optimization of scaffold design towards enhanced bone healing, for example in case of fracture, in particular in case of missing pieces of the fractured bone. The method comprises a first step of inputting a set of parameters, including information on the geometry of the scaffold and information on the material, into a computational model. The input of the set of parameters can be performed by selecting the set of parameters from a database, or another external source, such as a cloud service / system, or from multiple external sources. Furthermore, the set of parameters can also be input manually by means of a data input device. The set of parameters can be selected and then provided to the computational model.

[0011] The computational model can be stored in a non-transitory storage medium of the computer and can be executed by at least one processor of the computer.

[0012] The set of parameters may be contained in, derived from, or associated with image data acquired with a medical imaging device configured to perform magnetic resonance imaging, positron emission tomography, x-ray imaging, e.g., CT.

[0013] The computational model includes a finite element model and a mechano-biological computational model. The computational model is a method including a finite element model and a mechano-biological computational model. The finite element model can be constructed based on the geometry and loading conditions of the scaffold. The finite element model determines a set of mechanical information data corresponding to a set of input parameters by calculation or finite element analysis, and provides the mechano-biological computational model with the set of mechanical information data, where the mechano-biological computational model determines a regenerated bone volume from the set of mechanical information data. The finite element model is a method determines a set of mechanical information data corresponding to a set of input parameters by calculation or finite element analysis, and provides the mechano-biological computational model with the set of mechanical information data, where the mechano-biological computational model is a method for determining a regenerated bone volume from the set of mechanical information data.

[0014] The mechanobiology computational model can be an agent-based model, for example, as disclosed by Pierier-Metz et al. (2020). In addition, any model or method based on partial differential equations can also be used as a mechanobiology computational model. In the following, we will briefly describe the agent-based model.

[0015] Agent-based models include methods for describing individual cell behavior based on stochastic processes and mechano-biological stimuli calculated from mechanical information data, in particular outputs obtained from calculations performed by finite element models. Agent-based models are based on a 3D regular matrix or 3D grid, for example with 100 μm spacing, where each point on this grid can describe and represent one agent, which can be occupied by at most one cell of one of the following phenotypes: mesenchymal stromal cell "MSC", osteoblast "bone cell", chondrocyte "cartilage cell", fibroblast "fibrous tissue cell". Each agent can thus represent a single cell of one phenotype and the corresponding tissue associated with that phenotype, where the corresponding tissue can be granulation tissue, bone, cartilage or fibrous tissue, respectively.

[0016] Furthermore, a single agent can contain multiple cells as well as the corresponding tissues associated with each cell, for example if the distance between agents on the grid is larger than the expected size of a cell, and thus both cells and tissues can be represented in the agent-based model.

[0017] At the initial time point, which represents when the scaffold is implanted and the healing process begins, in the agent-based model, only the agents representing MSCs are taken into account in the simulation.

[0018] An agent representing an MSC can move at a given speed, such as 30 μm / h, on the grid. This migration process is implemented as an iterative random walk process, i.e., each new position adopted by the agent during the iteration step is randomly selected among the free positions adjacent to the agent's current position, which represents the current position of the corresponding cell. Additional constraints can be implemented in the agent-based model, such as surface guidance of migration. In that case, a new position is accessible by the agent only if it is adjacent to previously deposited tissue or to intact tissue or to the scaffold surface.

[0019] Each iteration step of the computational model corresponds to one healing day and corresponds to a predefined percentage, for example 30% MSC differentiation. The agent containing this percentage of MSCs to differentiate changes into different phenotypes depending on the mechanobiological stimulus. The different phenotypes can be selected from the group of osteoblasts, chondrocytes, fibroblasts or none, for stimuli favoring bone, cartilage, fibrous tissue and resorption, respectively. Since the agent can contain a cell type and a corresponding tissue, the differentiation step leads directly to the accumulation of tissue at the same location. Further constraints such as surface guidance of the tissue accumulation process can also be implemented. In that case, the agent representing MSCs can only differentiate if it is adjacent to previously accumulated or intact tissue or to the scaffold surface.

[0020] Finally, agents representing each cellular phenotype can proliferate or undergo apoptosis at a given rate, depending on the local stimulus: agents for which the local stimulus is favorable can proliferate, i.e. new agents representing new daughter cells of the same phenotype are created at the neighboring location, while other agents can undergo apoptosis, i.e. the corresponding agents representing the corresponding cells are removed from this agent's location.

[0021] Depending on the exact configuration of the computational models, including mechanobiological computational models, including agent-based models, and finite element models, the scaffold materials, additional therapies such as growth factors, the cellular activity levels, i.e., proliferation, differentiation, and apoptosis rates and migration rates, change to reflect the lack of biological stimulation corresponding to the large bone defect or improvement of the bone defect that may be due to beneficial materials or additional therapies.

[0022] The output of a mechanobiological computational model, for example an agent-based model, can be the regenerated bone volume after a time interval in a given region of interest, for example a scaffold hole, which corresponds to the expected time of healing or at least no further development of the defect situation. This value is calculated at the end of the simulation or calculation of the mechanobiological computational model by adding up all agents, including osteoblast "bone", and multiplying them by the size of one agent of a predefined size. This volume can be divided by the sum of the free volumes in the region of interest, for example excluding the scaffold, to obtain the percentage of bone volume.

[0023] Furthermore, another output of the mechanobiological computational model may be the calculation of the time required to achieve bone healing, where bone healing must be defined in terms of a predefined bone volume, which can be obtained, for example, from a database of medical data containing bone volumes corresponding to a particular bone with a corresponding defect, or the continuity of the regenerated bone in the defect.

[0024] The output of the mechanobiology model may be provided from the computer processor to a non-transitory storage medium and further displayed on a display for graphical visualization of the output.

[0025] In the second step of the method of the present invention, a plurality of regenerated bone volumes are determined for the plurality of sets of parameters by the first step, in particular to generate scaffold bone data that relate the regenerated bone volumes to the corresponding sets of parameters for which the computational model calculated the regenerated bone volumes. This second step can be performed or calculated in parallel or in series. In the case of parallel calculation of the second step, each regenerated bone volume for each corresponding set of parameters among the plurality of sets of parameters is determined by the first step at a time. However, in the case of serial calculation, one regenerated bone volume for one of the sets of parameters is determined by the first step at a time. That is, each corresponding regenerated bone volume for each corresponding set of parameters among the plurality of sets of parameters is determined one after the other in a sequential manner.

[0026] The third step of the method of the present invention is to determine a computational surrogate model comprising a parametric model configured to relate the regenerated bone volume to a set of parameters from the scaffold bone data. The computational surrogate model is a method comprising a parametric model. The parametric model can be in the form of a polynomial function, which can be obtained by an interpolation or curve fitting method that relates the regenerated bone volume as a function of the set of parameters from the scaffold bone data. The parametric model can also be in the form of a Gaussian function. This is advantageous because such a parametric model is computationally less expensive and faster to calculate than the computational models described above, including finite element models and mechanobiological computational models, that are used to calculate the regenerated bone volume for a set of parameters.

[0027] The fourth step of the method of the present invention includes determining the optimal set of parameters from the computational surrogate model that outputs the maximum regenerated bone volume.The advantage of this is that the scaffold design can be determined by the optimal set of parameters for enhancing bone healing.For example, the fourth step of the method of the present invention can be performed using a computational optimization model, where the computational optimization model is a method for globally optimizing an input-output function, and the input-output function is the mathematical expression obtained in the third step.

[0028] The method of the present invention allows for the optimization of scaffolds, such as 3D printed scaffolds, for enhanced bone regeneration. The method includes not only initial mechanical stimulation or initial mechanical properties, but also bone regeneration outcomes to optimize scaffold design. Furthermore, the use of computational surrogate models allows for a setup that can be run in a reasonable amount of time on a standard computer. Thus, the steps of the computer-executable method can be executed on at least one processor of a computer. Furthermore, due to the complexity and sheer amount of data that the processor must process and calculate, it may be advantageous to use an array of parallel processors to perform the calculations necessary to execute the steps of the method.

[0029] It is understood that additional intermediate steps, which may be apparent to a person skilled in the art, can also be carried out between any two successive steps of the method of the invention.

[0030] According to an embodiment of the present invention, each set of parameters may further include information about patient-specific data, including bone geometries obtained from medical images of the patient and load boundary conditions for the bone geometries. The bone geometries may include fractured bone geometries, e.g., where a part of the bone is missing. The load boundary conditions for the bone geometries may be obtained from the patient-specific medical data. The load boundary conditions may be applied based on an estimation of typical loads under walking conditions, typically for the patient's weight. Furthermore, the load boundary conditions may depend on the location of the fractured bone, i.e., the part of the body where the bone breakage occurred. Based on this, force types such as compressive load force, bending load force, torsional load force, or a combination thereof may be applied as the corresponding load boundary conditions.

[0031] In particular, the patient-specific data may include or be derived from image data acquired with a medical imaging device.

[0032] According to one embodiment of the invention, the first step of the method may further include combining a bone shape with a scaffold shape, and discretizing the bone shape combined with the scaffold shape into a computational grid of a finite element model.

[0033] The finite element model can be based on the shape of the defective bone to be treated with the scaffold. This composite shape can be simplified, especially with respect to the tip of the intact bone included, for example, as a circular or elliptical cylinder, or can be directly imported from image data, for example, using an X-ray image or a computed tomography "CT scan". Furthermore, the composite shape for the finite element model can preferably include the tip of the intact bone at least twice the length of the defect, the defect area, i.e., the area where the scaffold including the fixation plate(s) and screws will be implanted according to the surgical plan, and the scaffold shape.

[0034] This aforementioned composite geometry is discretized in finite element software as a computational mesh, which may include tetrahedral and / or hexahedral and / or polyhedral finite elements of suitable precision.

[0035] The following load boundary conditions can be implemented: - The distal tip of the bone can be fixed with no rotational or translational degrees of freedom. At the other extremity, a load can be applied, usually based on an estimate of the typical load under walking conditions for the weight of the patient under test.

[0036] Assuming that either all tissues and materials exhibit linear elastic behavior, or that biological tissues exhibit poroelastic behavior and plates, screws, and scaffolds exhibit linear elastic behavior, mechanical properties can be assigned to each part of the body corresponding to the site with the fracture.

[0037] Various parts of the body can be fused or joined together.

[0038] Mechanobiology computational models, e.g. agent-based models, can be coupled with finite element models in two ways. First, the cell behavior can be influenced with mechanical stimuli that can be derived element by element from the finite element analysis, and / or second, the material properties of the tissues can be updated in the finite element model at each iteration depending on the tissue distribution. More precisely, each element of the finite element model can be mapped to the agents it contains and its material properties can be defined as a weighted average of the tissues predicted with these agents, and the material properties can be further averaged over the last 10 iterations to take into account the accumulation and maturation of tissues as disclosed by Lacroix and Prendergast (2002). The finite element analysis and the agent-based simulation can be performed iteratively to predict the entire regeneration process, where one iteration can represent one day of the healing process.

[0039] In other words, a finite element model can be built based on the geometry of the defect to be treated and the patient's weight corresponding to the loading conditions. Then, iteratively, a simulation or calculation of the finite element model, i.e., a finite element analysis, can be performed. From the simulation or calculation of the finite element model, the local mechanics in each finite element corresponding to the area of ​​the patient's body where the bone destruction occurred can be determined. These mechanical values ​​can be used to calculate a mechanobiological stimulus, such as a linear combination of octahedral shear strain and fluid relative velocity, or a threshold for hydrostatic stress and minimum principal strain. Based on this stimulus, the cells implemented in the mechanobiological computational model, i.e., agent-based model, can take on specific behaviors, such as differentiation, apoptosis or cell death, proliferation, and migration. The cell distribution in the regenerated area will be used to update the material properties in each finite element, since each cell accumulates a specific tissue type with different material properties. Then, the finite element analysis can be performed again and the whole process can be performed iteratively, where one iteration can correspond to one healing day.

[0040] According to another embodiment of the present invention, the computational model, in particular the mechanobiological computational model, calculates the volume of regenerated bone as a function of time, where the computational model simulates, in particular iteratively, the changes in the cellular activity and the mechanical environment, e.g. loading force, over the healing process of bone regeneration. In this embodiment, the bone regeneration as a function of time can take into account the influence of dynamic changes on bone regeneration over the healing process. The regenerated bone volume that can be used for the computational surrogate model in the third step of the method of the present invention corresponds to the time point of the end of the healing process.

[0041] Furthermore, the set of parameters may include information about the degradation of the scaffold material over time, where the computational model may determine the regenerated bone volume, particularly in an iterative manner, depending on the degradation of the scaffold material. This would allow incorporating the dynamic interaction between the scaffold and bone regeneration by including the degradation of the scaffold material. The degradation of the scaffold may occur over a long time scale, such as after months or years, compared to the healing phase of a fracture, which is usually on the order of weeks.

[0042] According to another embodiment of the present invention, after the fourth step, the first step is performed again by inputting a set of optimal parameters determined by the computational surrogate model, such that an optimal regenerated bone volume is calculated from the computational model, and if the difference between the optimal regenerated bone volume and the maximum regenerated bone volume previously obtained from the computational surrogate model in the fourth step is less than 5% of the optimal regenerated bone volume determined by the computational model using the optimal set of parameters, the optimal set of parameters calculated in the fourth step is selected as the set of parameters for the scaffold design that promotes enhanced bone healing.

[0043] In other words, after determining the optimal set of parameters that the computational surrogate model outputs the maximum regenerated bone volume, the determined optimal set of parameters is input again to the computational model. Here, the computational model determines the regenerated bone volume. Simulations are performed again using the finite element model of the computational model and the mechanobiology computational model to determine the corresponding regenerated bone volume using the aforementioned optimal set of parameters. This regenerated bone volume calculated using the mechanobiology computational model corresponds to the optimal regenerated bone volume and is considered to be more accurate than the results from the computational surrogate model. The optimal regenerated bone volume determined by the mechanobiology computational model is compared with the maximum regenerated bone volume determined by the computational surrogate model to determine the degree of deviation from the optimal regenerated bone volume determined by the computational model, in particular the mechanobiology computational model and the computational surrogate model. If the result of the comparison shows that the difference is less than 5% of the optimal regenerated bone volume determined by the computational model using the optimal set of parameters, the optimal set of parameters calculated in the fourth step, i.e., the set of parameters using the computational surrogate model, is selected as the set of parameters for the scaffold design that promotes enhanced bone healing.

[0044] This has the advantage that the use of a computational surrogate model allows for a fast and computationally inexpensive determination of the optimal set of parameters that maximizes regenerated bone volume. Furthermore, further simulations using the determined optimal set of parameters using finite element methods and mechanobiology computational models will increase the reliability of the results obtained using the computational surrogate model. This therefore makes the method of the present invention overall computationally efficient and accurate.

[0045] Furthermore, if the difference obtained by the comparison is more than 5% of the optimal regenerated bone volume determined by the computational model using the optimal set of parameters, all four steps of the method of the present invention are carried out using a larger set of parameters, so as to obtain an improved computational surrogate model. This is done by obtaining a high sampling of the regenerated bone volume associated with the set of parameters, i.e., a higher sampling of the parameter space, and thus a highly sampled space of regenerated bone volume. This can increase the accuracy of the computational surrogate model, and therefore the accuracy of the entire method of the present invention.

[0046] The information regarding the scaffold shape can include information regarding scaffold pore size, and / or pore size distribution, and / or curvature. Additionally, the information regarding the scaffold material can include information regarding Young's modulus, and / or Poisson's ratio, and / or porosity, stiffness, and / or density of the scaffold material. Additionally, information regarding the scaffold material distribution can be provided, such as where Young's modulus, and / or Poisson's ratio, and / or porosity, and / or stiffness, and / or density are variable in different regions within the scaffold shape.

[0047] According to another embodiment of the present invention, the multiple sets of parameters are selected using a uniform sampling scheme or a Latin hypercube sampling scheme.

[0048] The Latin hypercube sampling method is a method configured to generate a set of parameter values ​​for a multidimensional space. For a size N, where N corresponds to the number of values ​​for each parameter in the multidimensional space, the multidimensional space is divided into subspaces with each side of the parameter space divided by N. Points are then randomly placed in the various subspaces that can be expanded to further dimensions such that there is exactly one point in each row and each column. This allows for sampling that is representative of the variability of the design space, further resulting in an accurate sparse representation of the full design space.

[0049] According to another embodiment of the present invention, the computed surrogate model is a Multivariate Adaptive Regression Splines (MARS) model or a Kriging model.

[0050] The MARS model is a non-parametric regression method that can be expressed as a product of hinge functions, such as piecewise linear functions, making the resulting computational surrogate model easy to interpret. Furthermore, a piece-wise cubic function can be adopted to implement the MARS model as a computational surrogate model. The MARS model is constructed by adding terms to maximally reduce the mean squared error until a certain tolerance level is reached, and then removing the least value-adding terms in the model to avoid overfitting. The MARS model can provide highly accurate results.

[0051] The Kriging model is a type of Gaussian process regression that calculates a weighted average of known points around a point of interest. The definition of these weights can be based on assumptions made about the covariance. When applying the Kriging model, different types of autocorrelation known to those skilled in the art can be defined, and the assumption of exponential autocorrelation can be used to obtain more accurate results.

[0052] Furthermore, the computational surrogate model may include a surrogate model such as a neural network model, or a radial basis function model, or a support vector machine model, or a Gaussian process regression model.

[0053] According to another embodiment of the present invention, a computational optimization model is used to determine the optimal set of parameters resulting in the maximum regenerated bone volume in the fourth step of the method of the present invention, wherein the computational optimization model is a computational optimization method selected from the group of a direct search algorithm, or a genetic algorithm, or a particle swarm optimization method.

[0054] Since the parametric model or the objective function based on the parametric model may contain some local optima, the computational optimization model may employ a global gradient-free optimization approach rather than a gradient-based optimization approach known to those skilled in the art. Thus, the computational optimization model may be selected from a family of gradient-free optimization approaches such as direct search algorithms, or genetic algorithms, or particle swarm optimization methods. These gradient-free optimization approaches or algorithms, when applied to the computational surrogate model, provide a more rapid assessment of the maximum regenerated bone volume compared to when applied directly to the mechanobiology computational model.

[0055] A second aspect of the present invention is a computer program and / or a computer program product comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the method of the present invention for performing optimization of scaffold design towards enhanced bone healing.

[0056] In particular the set of parameters may be provided by a computer program from a non-transitory storage medium of the computer, as detailed in the context of the first aspect of the invention. Furthermore, the non-transitory storage medium may comprise image data and / or patient-specific data. The image data and / or patient-specific data may be acquired or have been acquired by a medical imaging device configured to record the image data and / or patient-specific data, convert said data into digital data, and store or transmit said digital data (and also referred to as "such data") representative of the patient-specific data to a computer with a non-transitory storage medium. This may be achieved, for example, by any network connection connecting the medical imaging device and the computer.

[0057] Further, the computer running the computer program may be connected to a display configured to display any output of the computer program. A third aspect of the present invention is a method for manufacturing a scaffold designed using the steps of the method or computer program of the present invention for performing scaffold design optimization towards enhanced bone healing, wherein the method for manufacturing the scaffold is a 3D printing method or an injection molding method. In particular, the method of manufacturing comprises the step of generating a digital file configured and adapted to include instructions for an additive manufacturing device or system such that the additive manufacturing device or system may manufacture the scaffold as calculated by the method according to the present invention.

[0058] The term "3D printing" may be used synonymously with additive manufacturing method.

[0059] In particular, the method according to the first aspect can be extended to include steps of a method for manufacturing a scaffold. When the method is embodied in a computer program, a computer or computer system executing the computer program can be connected or configured to transmit a scaffold design resulting from execution of the method to an additive printing device or system, for example by converting the result into a file format suitable for execution by an additive manufacturing device or system.

[0060] The terms "computerized device," "computerized system," or similar terms refer to a device that includes one or more processors that are operable or that operate according to one or more programs.

[0061] The term "computer" or system thereof may be used herein in its normal context in the art - such as a general purpose processor or microprocessor, RISC processor, or DSP, and may include additional elements such as memory or communication ports. Optionally or additionally, the term "computer" or derivatives thereof may refer to a device that can execute a program provided or embedded therein, and / or control and / or access other devices, such as data storage devices and / or other devices such as input and output ports. The term "computer" may also refer to multiple processors or computers that are connected and / or linked and / or otherwise in communication, possibly sharing one or more other resources, such as a memory inform of a non-transitory storage medium.

[0062] As used herein, the terms "server" or "client" or "backend" refer to a computer or computerized device that provides data and / or operational services or services to one or more other computerized devices or computers.

[0063] The terms "software," "computer program," "software procedure" or "procedure," or "software code" or "code," or "application" or "app," may be used interchangeably depending on the context, and generally refer to a product or method that includes one or more instructions or instructions or circuitry for performing a sequence of operations that represent an algorithm and / or other process or method. The program may be stored on a medium such as a RAM, ROM, or disk, or may be embedded in accessible and executable circuitry such as a processor or other circuitry.

[0064] The processor and program may be comprised, at least in part, of the same device, such as an array of electronic gates, such as an FPGA or ASIC, designed to perform a sequence of programmed operations, optionally including or coupled to a processor or other circuitry.

[0065] As used herein, without limitation, a process refers to a collection of actions for achieving a particular purpose or result.

[0066] Similarly, a model may represent a collection of actions to achieve some particular goal or result.

[0067] The terms "configure" and / or "adapt" for a purpose, or variations thereof, encompass the use of at least software and / or electronic circuitry and / or auxiliary devices that are designed and / or implemented and / or operable or operative to accomplish a purpose.

[0068] An apparatus such as a non-transitory storage medium storing and / or comprising a computer program and / or data specifically constitutes an article of manufacture. Unless otherwise specified, the program and / or data are stored in or on the non-transitory medium.

[0069] In the context of embodiments of the present disclosure, by way of example and not limitation, terms such as "operate" or "perform" also encompass capabilities such as "operable" or "executable," respectively.

[0070] The present invention will now be described with reference to the embodiments shown in the accompanying drawings. [Brief description of the drawings]

[0071] [Figure 1] 1 shows a flow chart of one embodiment of a method of the present invention for performing scaffold design optimization towards enhanced bone healing. [Diagram 2] FIG. 1 shows a schematic diagram of a finite element model geometry consisting of the scaffold geometry and the bone geometry to be composited. [Diagram 3] FIG. 3 shows a schematic longitudinal cross-sectional view of the scaffold geometry shown in FIG. 2. [Figure 4] FIG. 4 shows a schematic longitudinal cross-sectional view of half of the scaffold shape shown in FIG. 3. [Diagram 5] FIG. 5 shows a top view of the scaffold shape shown in FIGS. 3 and 4. [Figure 6] 3 is a three-dimensional plot showing the percentage of regenerated bone volume versus a set of input parameters including pore size information for the scaffold geometry shown in FIG. 2. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0072] FIG. 1 is a flow chart showing an embodiment of the method of the present invention for performing optimization of scaffold design for enhanced bone healing. The method is a computer-implemented method. The method includes a first step a) of initially sampling a set of parameters including information on the geometry and material of the scaffold and inputting the set of parameters into a computational model. The sampling of parameters is obtained by the Latin Hypercube Sampling technique "LHS". The LHS technique is disclosed by Simpson et al. (2002). The computational model includes a finite element model and a mechanobiology computational model. The computational model calculates the regenerated bone volume using the input set of parameters.

[0073] In a second step b), a plurality of regenerated bone volumes are determined for a plurality of sets of parameters according to the first step a) to generate scaffold bone data that associates the regenerated bone volume with a corresponding set of parameters for which the computational model calculated the regenerated bone volume.

[0074] The third step c) of the method involves determining a computational surrogate model consisting of a parametric model configured to relate the regenerated bone volume to a set of parameters from the scaffold bone data. As computational surrogate model, a Kriging model is used, which is implemented using Matlab's Kriging toolbox DACE, as disclosed by Lophaven et al. (2002).

[0075] The method includes a fourth step d) of using a computational optimization model to determine an optimal set of parameters for which the computational surrogate model outputs the maximum volume of regenerated bone. The computational optimization model can be implemented, for example, using the Matlab Global optimization toolbox disclosed by The MathWorks, Inc. in 2020.

[0076] An exemplary embodiment of the method includes a fifth step e) in which the computational model calculates the optimal regenerated bone volume using the optimal set of parameters determined by the computational surrogate model in the fourth step d) of the method.

[0077] In a sixth step f) of the exemplary method, the difference between the optimal regenerated bone volume obtained from the computational model of the fifth step e) and the maximum regenerated bone volume obtained from the computational surrogate model of the fourth step d) is calculated. This sixth step f) checks whether the difference is less than 5% of the optimal regenerated bone volume determined by the computational model with the optimal set of parameters. If the difference is more than 5% of the optimal regenerated bone volume, the method then returns to the third step c), as indicated by the first arrow N1. Steps c) to e) are performed with more sets of parameters to obtain an improved computational surrogate model by obtaining a higher sampling of the regenerated bone volume associated with the set of parameters.

[0078] After each repetition of steps c) to e), a sixth step f) of the method is performed, in which the method checks each time whether the difference is less than 5% of the optimal regenerated bone volume determined by the computational model with the optimal set of parameters. Steps c) to f) are repeated until the difference is less than 5% of the optimal regenerated bone volume, in which case the method proceeds to a seventh step g), as indicated by the second arrow Y1.

[0079] In the seventh step g) of the method, it is checked whether the optimal regenerated bone volume is better, e.g. higher, than all previously stored values. If the check shows that the optimal regenerated bone volume is not better, e.g. higher, than all previously stored values, the method then returns to the third step c), as indicated by the third arrow N2. After carrying out steps c) to f), if the condition of the sixth step f) is satisfied, the seventh step g) is then carried out. This repetition is carried out until it is found that the optimal regenerated bone volume is better, e.g. higher, than all previously stored values. In this case, as indicated by the fourth arrow Y2, the method has finally determined a set of parameters of the final optimized scaffold design h), in which enhanced bone healing is achieved.

[0080] FIG. 2 shows a cross-sectional view of a finite element model geometry 1 for simulation or calculation using a finite element model, i.e., finite element analysis, where the finite element model geometry 1 is the geometry used in the finite element analysis. The finite element geometry 1 comprises a bone geometry 2 comprising the geometry of cortical bone 4 and bone marrow 5. The finite element model geometry 1 further comprises the geometry of a scaffold 3, a steel support structure 6, also called a plate fixation system, and granulation tissue 7 surrounding the geometry of the scaffold 3, the bone geometry 2, and the steel support structure 6. A symmetry line 8 indicates that the finite element model geometry is symmetrical about the symmetry line 8, in which case the finite element simulation can be performed considering only half of the finite element model geometry 1, since the boundary conditions corresponding to the symmetry can be considered. That is, the finite element simulation can be performed considering only half of the finite element model geometry 1, while the results of the simulated half can be assumed to be the same for the other half of the finite element model geometry 1, and the results are mapped to be reflected around the symmetry line 8.

[0081] FIG. 3 is a schematic longitudinal cross-sectional view showing the shape of the scaffold 3. The scaffold 3 has a cylindrical shape having a length l and a width w along the longitudinal direction, and the width in this case corresponds to the diameter of the scaffold 3.

[0082] FIG. 4 is a longitudinal cross-sectional view of half of the scaffold 3 of FIG. 3, assuming symmetry as depicted by the line of symmetry 8 of FIG.

[0083] The pores at the ends of the cylindrical scaffold 3 have a length x2, while the central pores along the longitudinal direction, i.e., those on the line of symmetry 8, have a length x1. A linear distribution of pore sizes is considered from the longitudinal length x1 to length x2, i.e., half the length l / 2 of the scaffold 3. The corresponding length of each pore distributed radially at a given distance from the line of symmetry 8 is assumed to be uniform, corresponding to the length of the pore size at that distance.

[0084] FIG. 5 is a top view of the scaffold 3 configuration of FIGS. 3 and 4, where each hole has a length x3 along the circumference.

[0085] Figure 6 shows a three-dimensional plot 9 of the percentage of regenerated bone volume along the z-axis z. The x-axis x shows the distribution of the input parameter, where the length in millimeters x1 of the scaffold shown in Figures 3 and 4 is varied. The y-axis y shows the distribution of the input parameter, where the length in millimeters x2 of the scaffold 3 shown in Figures 3 and 4 is varied.

[0086] As described by the first step a) and the second step b) of the method, the first step a) determines a plurality of regenerated bone volumes for a set of a plurality of parameters, such that the computational model generates scaffold bone data represented by a plurality of dots 10 relating the regenerated bone volume to a corresponding set of parameters for which the computational model calculated the regenerated bone volume. The plurality of dots 10 are plotted in a three-dimensional plot, each of which represents a corresponding percentage of regenerated bone volume corresponding to a set of parameters of the shape of the scaffold 3 based on the lengths x1 and x2.

[0087] As described in the third step c) of the method, a computational surrogate model relates the regenerated bone volume with a set of parameters from the scaffold bone data to generate a parametric model, here represented by surface 11.

[0088] In a fourth step d), a computational optimization model is used to determine an optimal set of parameters that results in a computational surrogate model that outputs the maximum regenerated bone volume as indicated by a peak 12 on the surface 11 .

[0089] List of codes Finite element model geometry 1 bone shape 2 Scaffold 3 cortical bone 4 Bone Marrow 5 steel support structure 6 Granulation tissue 7 Line of symmetry 8 3D Plot 9 Dot 10 surface 11 Peak 12 First step a Second step b Third step c The fourth step d The fifth step e The sixth step f The seventh step g Optimized scaffold design h Scaffold shape length l Scaffold width w X-axis x Y-axis y Z-axis z Minimum hole length x1 Maximum hole length x2 Hole width x3 First Arrow N1 Second Arrow Y1 Third Arrow N2 4th Arrow Y2

[0090] JPEG2025501668000002.jpg216153JPEG2025501668000003.jpg227153JPEG2025501668000004.jpg208153JPEG2025501668000005.jpg113153

Claims

1. A method, in particular a computer-implemented method, for carrying out optimization of scaffold design (h) towards enhanced bone healing, comprising the following steps: a) inputting a set of parameters including information on the shape and material of the scaffold (3) into a computational model, the computational model including a finite element model and a mechanobiology computational model, the finite element model determining a set of mechanical information data for the set of parameters and providing it to the mechanobiology computational model, the mechanobiology computational model determining a regenerated bone volume from the set of mechanical information data; b) determining a plurality of regenerated bone volumes for a plurality of sets of parameters according to step a) to generate scaffold bone data relating the regenerated bone volumes to corresponding sets of parameters; c) determining a computational surrogate model comprising a parametric model configured to relate the regenerated bone volume to a set of parameters from the scaffold bone data; and d) determining an optimal set of parameters from the computational surrogate model that outputs the maximum regenerated bone volume; The method comprising:

2. The method of claim 1 , wherein each set of parameters further comprises information about patient-specific data, the patient-specific data comprising a bone geometry (2) and loading boundary conditions of the bone geometry, the bone geometry being obtained from medical images of the patient.

3. 3. The method according to claim 2, wherein step a) of the method further comprises: combining the bone shape (2) with a shape of the scaffold (3) and discretizing the bone shape (2) combined with the shape of the scaffold (3) into a computational grid of a finite element model.

4. 4. The method of claim 2 or 3, wherein the computational model calculates regenerated bone volume as a function of time, and the computational model simulates changes in cellular activity and mechanical environment over the healing course of bone regeneration.

5. 5. The method of claim 4, wherein the set of parameters includes information regarding degradation of a scaffold material over time, and the computational model determines regenerated bone volume dependent on the degradation of the scaffold material.

6. The method according to any one of claims 1 to 5, wherein after step d), step a) is performed by inputting an optimal set of parameters determined by a computational surrogate model such that an optimal regenerated bone volume is calculated from the computational model, and where if the difference between the optimal regenerated bone volume and the maximum regenerated bone volume obtained from the computational surrogate model of step d) is less than 5% of the optimal regenerated bone volume determined by the computational model using the optimal set of parameters, the optimal set of parameters calculated in step d) is selected as the set of parameters for the scaffold design that promotes enhanced bone healing.

7. The method of claim 6, wherein if the difference obtained by the comparison exceeds 5% of the optimal regenerated bone volume determined by the computational model using the optimal set of parameters, steps a) to d) are performed using more sets of parameters to obtain an improved computational surrogate model.

8. The method according to any one of claims 1 to 7, wherein the information on the shape of the scaffold (3) comprises information on the pore sizes (x1, x2, x3) and / or the pore size distribution and / or the curvature of the scaffold (3).

9. The method according to any one of claims 1 to 8, wherein the information relating to the material of the scaffold comprises information on Young's modulus, and / or Poisson's ratio, and / or porosity, and / or stiffness, and / or density of the material of the scaffold.

10. The method according to any one of claims 1 to 9, wherein the set of parameters is selected using a uniform sampling scheme or a Latin Hypercube sampling scheme.

11. The method according to any one of claims 1 to 10, wherein the calculated surrogate model is a multivariate adaptive regression spline model or a Kriging model.

12. The method according to any one of claims 1 to 11, wherein in step d) a computational optimization model is used to determine the optimal set of parameters resulting in the maximum regenerated bone volume, the computational optimization model being selected from the group of direct search algorithms or genetic algorithms or particle swarm optimization methods.

13. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method according to any one of claims 1 to 12.

14. A method for manufacturing a scaffold designed with the steps of the method according to any one of claims 1 to 12, wherein the method for manufacturing the scaffold (3) is a 3D printing method or an injection molding method.

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